Mathematical Sciences: Supplement To: Ergodic Theory, Groupsand Geometry - Differential Geometry and Dynamical Systems by: Renato Feres

数学科学：补充：遍历理论、群和几何 - 微分几何和动力系统作者：Renato Feres

• 批准号: 9203505
• 负责人: Robert Zimmer
• 金额: $ 2.7万
• 依托单位: University of Chicago
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-06-15 至 1994-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9203505&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Supplement; Ergodic; Theory

Feres will study several problems in differential geometry and dynamical systems whose aim is to understand certain phenomena of rigidity of group actions. The solution to these problems could shed some light on a general conjecture of Zimmer's concerning actions of higher rank lattice groups and improve certain aspects of Gromov's theory of rigid transformation groups in the special case when such groups possess elements that define dynamical systems with hyperbolic behavior. This project involves research in ergodic theory. Ergodic theory in general concerns understanding the average behavior of systems whose dynamics is too complicated or chaotic to be followed in microscopic detail. Under the heading "dynamics can be placed the modern theory of how groups of abstract transformations act on smooth spaces. In this way ergodic theory makes contact with geometry in its quest to classify flows on homogeneous spaces.

费雷斯将研究微分几何中的几个问题 和动力学系统，其目的是了解某些 群体行动的刚性现象。 解决这些 这些问题可能会揭示一个普遍的猜想， Zimmer关于高阶格群的作用和 对Gromov刚性理论某些方面改进 变换群在特殊情况下，当这样的群 拥有定义双曲型动力系统的元素 行为 这个项目涉及遍历理论的研究。 遍历 理论一般涉及理解的平均行为， 动态过于复杂或混乱的系统 在微观细节上进行跟踪。 在“动态”标题下， 可以把现代理论放在抽象的 变换作用于光滑空间。 这样遍历理论 与几何学接触，以寻求对 齐性空间